1. Foundations for Algebra
Chapter 1
Foundations for Algebra

2. LT1 - Write Expressions
Write an algebraic for the following verbal statements:
3 more than twice a number x
9 less than the quotient of 6 and a number y
the product of 4 and the sum of a number z and 7

3. Anatomy of a Term
coefficient
exponent
5x4
base

4. LT2 - Order of Operations
G - Grouping symbols
E - Exponents
MD - Multiply and divide (from left to right)
AS - Add and subtract (from left to right)

5. LT2 - Order of Operations
Evaluate the expression

6. LT2 - Order of Operations
Evaluate if x = 5 and y = 2

7. LT3 - Estimate a Square Root
Estimate to the nearest whole number

8. Warmup - Estimate
Estimate to the nearest integer

9. LT4 - Classify Real Numbers
Rational Number
any number that can be expressed as the quotient of two integers
Natural Numbers {1, 2, 3,...}
Whole Numbers {0, 1, 2,...}
Integers {..., -2, -1, 0, 1, 2,...}
Irrational Number
a number that can’t be expressed rationally
Does not terminate
Does not repeat

10. LT4 - Classify Real Numbers

11. LT5&6 - Order and Graph Real #’s
Graph and order the following real numbers from least to greatest:

12. LT7 - Properties of Real #’s

13. LT7 - Properties of Real #’s

14. LT8 - Simplify an Expression
Simplify the following expressions

15. LT9 - Add/Subtract Real #’s

16. LT9 - Add/Subtract Real #’s
Evaluate each expression

17. LT9 - Add/Subtract Real #’s
Evaluate each expression

18. LT9 - Add/Subtract Real #’s
Evaluate each expression
1/3 - 2/5 + 14/30

19. LT9 - Multiply Real #’s

20. LT9 - Divide Real #’s

21. LT9 - Multiply/Divide Real #’s
Sign
Positive
Negative + -

22. LT9 - Multiply/Divide Real #’s
Evaluate each expression
(11)(-5)
(-4)(3)(-6)
(-7)(-15)(-2)

23. LT9 - Inverses

24. LT10 - Distributive Property
Simplify using the Distributive Property
3(3 + 4)
2(x + 7)
-4(2 - 8)
2x(3x - 2y)

25. Warmup - Simplify Simplify the following expressions
3(x y) - 2(x - y)
-(-x - y - z) - (-x - y - z)
3x2y + 2xy + 3xy2 - 2yx - 3x2y - 3xy2

26. Warmup - Always, Sometimes, Never
x - 2 is greater than x
7 + x = x + 7
13 - x = x - 13
Absolute value of x is greater than x
100 duck-sized horses defeat 1 horse-sized duck in battle

27. LT11 - Solutions to 1 Variable
Determine whether the given value satisfies the equation
3x (2x + 5) = 15, x = 13
-¼(6x + 20) = -7, x = 2
x = -5, x = -2

28. LT12 - Solutions to 2 Variables
Determine whether the given coordinate pair satisfies the equation
y = 2x + 7, (-14, -35)
3x + 2y = 6, (6, -6)
y - 4 = ⅔(x + 7), (-13, 0)

29. LT13 - Relationships
Represent the following relationship as an equation, a table, and a graph
Three more than twice a number x is equal to y

30. LT13 - Relationships Three more than twice a number x is equal to y
Equation:

31. LT13 - Relationships Three more than twice a number x is equal to y
Table: x y

32. LT13 - Relationships Three more than twice a number x is equal to y
Graph:

33. LT13 - Relationships Rule of Four Verbal Equation
Three more than twice a number x is equal to y 2x + 3 = y
Table Graph x y -2 -1 1 3 5 2 7